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Jul 20, 2013
07/13

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Spiros A. Argyros

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The class of countably intersected families of sets is defined. For any such family we define a Banach space not containing $\ell^{1}(\NN )$. Thus we obtain counterexamples to certain questions related to the heredity problem for W.C.G. Banach spaces. Among them we give a subspace of a W.C.G. Banach space not containing $\ell^{1}(\NN )$ and not being itself a W.C.G. space.

Source: http://arxiv.org/abs/math/9210210v1

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Jul 20, 2013
07/13

by
Spiros A. Argyros; V. Felouzis

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It is shown that every Banach space either contains $\ell ^1$ or it has an infinite dimensional closed subspace which is a quotient of a H.I. Banach space.Further on, $L^p(\lambda )$, $1

Source: http://arxiv.org/abs/math/9712277v1

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Jul 20, 2013
07/13

by
Spiros A. Argyros; Irene Deliyanni

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Two examples of asymptotic $\ell_{1}$ Banach spaces are given. The first, $X_{u}$, has an unconditional basis and is arbitrarily distortable. The second, $X$, does not contain any unconditional basic sequence. Both are spaces of the type of Tsirelson. We thus answer a question raised by W.T.Gowers.

Source: http://arxiv.org/abs/math/9407210v1

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Sep 23, 2013
09/13

by
Spiros A. Argyros; Kevin Beanland

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It is shown that for each separable Banach space $X$ not admitting $\ell_1$ as a spreading model there is a space $Y$ having $X$ as a quotient and not admitting any $\ell_p$ for $1 \leq p < \infty$ or $c_0$ as a spreading model. We also include the solution to a question of W.B. Johnson and H.P. Rosenthal on the existence of a separable space not admitting as a quotient any space with separable dual.

Source: http://arxiv.org/abs/1111.4714v1

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Sep 24, 2013
09/13

by
Spiros A. Argyros; Pavlos Motakis

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A reflexive hereditarily indecomposable Banach space $\mathfrak{X}_{_{^\text{ISP}}}$ is presented, such that for every $Y$ infinite dimensional closed subspace of $\mathfrak{X}_{_{^\text{ISP}}}$ and every bounded linear operator $T:Y\rightarrow Y$, the operator $T$ admits a non-trivial closed invariant subspace.

Source: http://arxiv.org/abs/1111.3603v3

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Sep 19, 2013
09/13

by
Spiros A. Argyros; Irene Deliyanni

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To any pair ( M , theta ) where M is a family of finite subsets of N compact in the pointwise topology, and 0{1/n} then T_M^theta is reflexive. Moreover, if the Cantor-Bendixson index of M is greater than omega then T_M^theta does not contain any l^p, while if the Cantor-Bendixson index of M is finite thenT_M^theta contains some l^p or c_o . In particular, if M ={ A subset N : |A| leq n } and {1/n}

Source: http://arxiv.org/abs/math/9207206v1

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Sep 23, 2013
09/13

by
Spiros A. Argyros; Pavlos Motakis

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It is shown that for every $k\in\mathbb{N}$ and every spreading sequence $\{e_n\}_{n\in\mathbb{N}}$ that generates a uniformly convex Banach space $E$, there exists a uniformly convex Banach space $X_{k+1}$ admitting $\{e_n\}_{n\in\mathbb{N}}$ as a $k+1$-iterated spreading model, but not as a $k$-iterated one.

Source: http://arxiv.org/abs/1105.2714v1

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Sep 22, 2013
09/13

by
Spiros A. Argyros; Pavlos Motakis

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Examples of non separable reflexive Banach spaces $\mathfrak{X}_{2^{\aleph_0}}$, admitting only $\ell_1$ as a spreading model, are presented. The definition of the spaces is based on $\alpha$-large, $\alpha

Source: http://arxiv.org/abs/1302.0715v1

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Sep 23, 2013
09/13

by
Spiros A. Argyros; Giorgos Petsoulas

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It is shown that variants of the HI methods could yield objects closely connected to the classical Banach spaces. Thus we present a new $c_0$ saturated space, denoted as $\mathfrak{X}_0$, with rather tight structure. The space $\mathfrak{X}_0$ is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure. Everyone is either of type I, namely, contains an isomorph of $\mathfrak{X}_0$ itself or else is isomorphic to a subspace of $c_0$ (type...

Source: http://arxiv.org/abs/1012.2758v1

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Sep 17, 2013
09/13

by
Spiros A. Argyros; Theocharis Raikoftsalis

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It is shown that every separable reflexive Banach space is a quotient of a reflexive Hereditarily Indecomposable space, which yields that every separable reflexive Banach is isomorphic to a subspace of a reflexive Indecomposable space. Furthermore, every separable reflexive Banach space is a quotient of a reflexive complementably $\ell_p$ saturated space with $1

Source: http://arxiv.org/abs/1003.0870v1

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Sep 23, 2013
09/13

by
Spiros A. Argyros; Irene Deliyanni

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A non RNP Banach space E is constructed such that $E^{*}$ is separable and RNP is equivalent to PCP on the subsets of E.

Source: http://arxiv.org/abs/math/9201222v1

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Sep 23, 2013
09/13

by
Spiros A. Argyros; S. Merkourakis; A. Tsarpalias

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It is proved that every normalized weakly null \sq\ has a sub\sq\ which is convexly unconditional. Further, an Hierarchy of summability methods is introduced and with this we give a complete classification of the complexity of weakly null \sq s.

Source: http://arxiv.org/abs/math/9512209v1

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Sep 19, 2013
09/13

by
Spiros A. Argyros; Kevin Beanland; Theocharis Raikoftsalis

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We construct a weak Hilbert Banach space such that for every block subspace $Y$ every bounded linear operator on Y is of the form D+S where S is a strictly singular operator and D is a diagonal operator. We show that this yields a weak Hilbert space whose block subspaces are not isomorphic to any of their proper subspaces.

Source: http://arxiv.org/abs/0910.4401v1

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Sep 23, 2013
09/13

by
Spiros A Argyros; Richard G Haydon

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We construct a hereditarily indecomposable Banach space with dual isomorphic to $\ell_1$. Every bounded linear operator on this space has the form $\lambda I+K$ with $\lambda$ a scalar and $K$ compact.

Source: http://arxiv.org/abs/0903.3921v2

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Sep 22, 2013
09/13

by
Spiros A. Argyros; Pandelis Dodos; Vassilis Kanellopoulos

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The present work consists of three parts. In the first one we determine the prototypes of separable Rosenthal compacta and we provide a classification theorem. The second part concerns an extension of a theorem of S. Todorcevic. The last one is devoted to applications.

Source: http://arxiv.org/abs/0805.2032v1

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Sep 22, 2013
09/13

by
Spiros A. Argyros; Irene Deliyanni; Denka Kutzarova; A. Manoussakis

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We study the modified and boundedly modified mixed Tsirelson spaces $T_M[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ and $T_{M(s)}[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ respectively, defined by a subsequence $({\cal F}_{k_n})$ of the sequence of Schreier families $({\cal F}_n)$. These are reflexive asymptotic $\ell_1$ spaces with an unconditio- nal basis $(e_i)_i$ having the property that every sequence $\{ x_i\}_{i=1}^n$ of normalized disjointly supported vectors contained in $\langle...

Source: http://arxiv.org/abs/math/9704215v1

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Sep 17, 2013
09/13

by
Spiros A. Argyros; Alexander D. Arvanitakis; Andreas G. Tolias

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In the present work we provide a variety of examples of HI Banach spaces containing no reflexive subspace and we study the structure of their duals as well as the spaces of their linear bounded operators. Our approach is based on saturated extensions of ground sets and the method of attractors.

Source: http://arxiv.org/abs/0807.2392v1

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Sep 17, 2013
09/13

by
Spiros A. Argyros; Irene Deliyanni; Andreas G. Tolias

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We construct a Hereditarily Indecomposable Banach space $\eqs_d$ with a Schauder basis \seq{e}{n} on which there exist strictly singular non-compact diagonal operators. Moreover, the space $\mc{L}_{\diag}(\eqs_d)$ of diagonal operators with respect to the basis \seq{e}{n} contains an isomorphic copy of $\ell_{\infty}(\N)$.

Source: http://arxiv.org/abs/0807.2388v1

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Sep 21, 2013
09/13

by
Spiros A. Argyros; Irene Deliyanni; Andreas G. Tolias

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We provide a characterization of the Banach spaces $X$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ which have the property that the dual space $X^*$ is naturally isomorphic to the space $\mathcal{L}_{diag}(X)$ of diagonal operators with respect to $(e_n)_{n\in\mathbb{N}}$ . We also construct a Hereditarily Indecomposable Banach space ${\mathfrak X}_D$ with a Schauder basis $(e_n)_{n\in\mathbb{N}}$ such that ${\mathfrak X}^*_D$ is isometric to $\mathcal{L}_{diag}({\mathfrak X}_D)$ with these...

Source: http://arxiv.org/abs/0902.1646v1